On homomorphisms indexed by semistandard tableaux

Abstract

We study the homomorphism spaces between Specht modules for the Hecke algebras $\h$ of type $A$. We prove a cellular analogue of the kernel intersection theorem and a $q$-analogue of a theorem of Fayers and Martin and apply these results to give an algorithm which computes the homomorphism spaces $\Hom_{\h}(S^μ,S^λ)$ for certain pairs of partitions $\lambda$ and $\mu$. We give an explicit description of the homomorphism spaces $\Hom_\h(S^μ,S^λ)$ where $\h$ is an algebra over the complex numbers, $\lambda =({\lambda }_1,{\lambda }_2)$ and $\mu$ is an arbitrary partition with ${\mu }_1\ge {\lambda }_2$.

32 pages. This third version of the paper contains some comments on homomorphisms between the Specht modules defined by Dipper and James and has a more rigorous proof of the result following Proposition 4.1

References in corpus (1)

• Homomorphisms Between Specht Modules of the Ariki Koike Algebra

Cited by in corpus (1)

• Homomorphisms Between Specht Modules of the Ariki Koike Algebra